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I think the problem is ambiguous as stated. There are many planes you could pick through the centre of mass that divides the atoms into two groups. Some other rule is needed to decide which is the "right" one. My guess is that what you have in mind involves finding the "longest" axis of the molecule in some sense. That's easy to determine visually, but not so easy when all you have to work with is numbers. One approach would be to find the axis around which the molecule has the smallest moment of inertia. That involves finding the eigenvectors of the rotational inertia matrix and picking the one with the smallest eigenvalue. -- Greg

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